本文探讨了技术进步普遍遵循指数增长的规律。作者引用了Daniel Eth的观点，指出技术发展中“输入”与“输出”之间存在幂律关系，这意味着投入的指数级增长会带来时间维度的平滑指数级增长。这种现象在成本效益、GDP增长、AI效率提升等方面均有体现。理论上，随着新想法的稀缺性增加，持续的进步需要指数级的投入。文章还分析了AI领域投入（如资本、算力、研究人员）的指数级增长原因，包括外部底层输入的指数增长（如摩尔定律）以及AI发展驱动的炒作效应。尽管摩尔定律将继续，但AI算力的大规模扩展可能在2030年前放缓，这意味着AI的整体进展速度在2020年后可能会有所减缓，但仍将保持较快速度。作者预测，AI将以类似方式解决目前尚不擅长的复杂任务，只是所需时间更长。

💡 指数增长是技术进步的默认模式：文章核心观点是，任何形式的技术增长，一旦开始，其趋势往往是指数级的。这基于“输入”与“输出”之间的幂律关系，即投入的指数级增长会带来时间维度的平滑指数级增长，在半对数坐标上呈现为一条直线。这种增长模式在技术成本下降、经济增长、AI效率提升等多个领域都有体现。

🚀 AI领域投入的指数级增长及其驱动因素：AI研发的投入，包括资金、算力、研究人员数量等，正呈现近似指数级的增长。这主要由两个因素驱动：一是外部底层输入的指数增长，例如摩尔定律所描述的计算能力成本下降；二是AI技术本身的进步驱动了市场炒作，进而吸引了更多的研究人员和投资。

⏳ AI解决复杂任务的时间尺度与进展预测：作者预测，AI将以与解决“干净、可验证”任务类似的方式，逐步攻克当前尚不擅长的“混乱”任务。只是这些任务的时间尺度会更长。虽然摩尔定律会持续，但用于AI的算力规模化扩张可能在2030年前达到瓶颈，尤其是在2028年后可能放缓。因此，若未在2030年前实现通用人工智能（TAI），AI的整体进展速度相较于2020年代可能会有所减慢，但仍将保持相当快的速度。

Published on September 29, 2025 4:13 PM GMT

Following in the tradition of @Algon, which linkposted an important thread from Daniel Eth about how AI companies are starting to seriously lobby, and have gotten early successes, I'll linkpost another thread from Daniel Eth, this time about how exponential increases are the default form of increase, assuming something's increasing at all.

In essence, I'm providing the theory for this post Almost all growth is exponential growth.

My sense is there’s generally a power law between “inputs” and “outputs” to technological progress. In this context, that manifests as “exponential increases in inputs over time yields smooth exponential increase in time horizons over time” (ie straight line on semi-log plot)

Why should there be a power law? We actually see this sort of dynamic come up all the time in technological progress - from experience curve effects (think declining PV prices) to GDP growth to efficiency improvements in various AI domains over time to AI scaling laws

And there are theoretical reasons to expect a power law, too. If ideas get harder to find over time, exponential inputs are needed for “consistent” progress. If each idea provides some proportionate improvement, then “consistent” progress cashes out as exponential growth.

I go into some detail defending a view along these lines in the appendix of my report w/ @TomDavidsonX on a software intelligence explosion. The point there was justifying the formulation of ‘r’, but it also may explain the METR Evals result

Will AI R&D Automation Cause a Software Intelligence Explosion?

So then if there’s a power law, the question becomes “is there exponential growth in inputs, and if so, why?” This seems more clearly true (approximately) - considering investment capital, to compute, to researchers in the field, etc

Okay, but why? Couple reasons. There’s exponential growth in some underlying inputs from the outside world (eg Moore for compute costs) - incidentally, I’d argue a similar power law explains that! Second, AI improvement drives hype which drives more researchers & investment

Now, this second reason is a bit fuzzier, since hype could drive non-exponential growth. Empirically, investment & number of researchers do seem to be growing ~exponentially. Same with decisions of scaling up large training runs by multiples of previous runs.

BTW, this is why I'm predicting the messier tasks faced by AI, where they currently struggle will be on the same curve, it's just that their time horizons currently are much shorter.

So AI will conquer the messy tasks similarly to how they've essentially conquered the clean, verifiable tasks, it will just take somewhat longer.

One caveat is that while Moore's law will still continue for the next 2 decades at least, the very fast compute scale-up driven by allocating more compute that we currently have to AI will not extend past 2030, and it's very plausible that it already slows down by 2028, so conditional on us not reaching TAI in 2030, progress in AI will be slower than in the 2020s (though still decently fast).

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